Having read through the recent publication "Analysis of Seven Years of Globe at Night Data", JJ Birriel, et. al. (JAAVSO vol. 42, 2014), I am pleased to see the results of this significant worldwide study on trends in night sky brightness. However, I think one of their main conclusions, that "over the period from 2006 to 2012 global averages of NELMs have remained essentially constant" is not properly supported by their data analysis.
Specifically, their conclusions based upon the statistical analysis of the NELM trend from 2006 to 2012 in Figure 3, appear to be faulty. The problem is they use a simple linear regression on data that is clearly not "straight-line" to get a correlation coefficient of R^2 = 0.6 yielding a p-value = .041, which they claim is not significant enough (at the 3 sigma level) to justify the conclusion that NELM values have been decreasing.
However, visual inspection of the plot, shows a marked drop in NELM values (approx. - 0.4) from 2006-10 to 20011-12 intervals. Also, a residual vs. fits plot of their linear regression shows a clear systematic over-under bias of the straight line fit, rather than a nice random spread of the data, as would be seen if a good model was used to fit the data.
I used Excel to do a basic second order regression on the data (plot attached), and get an R^2 = 0.85 which corresponds to a p-value = 0.003, which is significant at the 3 sigma level. A better model such as this second order fit matches the observations more cleanly, and would provide statistical support of the more reasonably obvious conclusion, that the global averages of NELM have in fact declined significantly over the period 2006 to 2102.
I hope the authors will take note of this issue, and correct the analysis of the data, particularly as shown in the regression on Figure 3.